Meta analysis with potentially correlated marketing study results

Across marketing studies, often the same hypothesis is tested many times. Study results, however, are not necessarily consistent. A meta analysis can be used to summarize results from the various studies, investigating why they differ. One of the assumptions often made in a meta analysis is that the study results are independent of one another. However, in many marketing analyses, different studies may share part of the same data set for the model estimation or one model could be a subset of the other so that results could be potentially correlated. Yet resulting correlation coefficients are not available. For such cases, we suggest three estimators which do not require correlation information. We take a case of advertising analyses, using a Monte-Carlo simulation to evaluate how neglecting the potential correlation affects the result of a meta analysis with covariates. The results of the simulation study indicate that eliminating the variance due to random error in study effect, instead of the correlation, may have a significant effect on the performance of estimators, when a relatively small number of study results are combined. This suggests that the ordinary least square estimator, which ignores potential heterogeneity due to estimation error but considers the random error, would not be a bad choice for a meta analysis in view of its easy implementation.